Pressure-induced collapse of the spin-orbital Mott state in the hyperhoneycomb iridate $\beta -{\mathrm{Li}}_2{\mathrm{IrO}}_3$

Hyperhoneycomb iridate $\beta -{\mathrm{Li}}_2{\mathrm{IrO}}_3$ is a three-dimensional analog of two-dimensional honeycomb iridates, such as $\alpha -{\mathrm{Li}}_2{\mathrm{IrO}}_3$, which recently appeared as another playground for the physics of Kitaev-type spin liquid. $\beta -{\mathrm{Li}}_2{\mathrm{IrO}}_3$ shows a noncollinear spiral ordering of spin-orbital-entangled $J_{\mathrm{eff}}=1/2$ moments at low temperatures below 38 K, which is known to be suppressed under a pressure of $\sim 2$ GPa. In addition, a structural transition is observed at $P_{\mathrm{S}}\sim 4$ GPa at room temperature. Using the neutron powder diffraction technique, the crystal structure in the high-pressure phase of $\beta -{\mathrm{Li}}_2{\mathrm{IrO}}_3$ above $P_{\mathrm{S}}$ was refined, which indicates the formation of ${\mathrm{Ir}}_2$ dimers on the zigzag chains, with an Ir-Ir distance of $\sim 2.66\AA$, even shorter than that of metallic Ir. We argue that the strong dimerization stabilizes the bonding molecular-orbital state comprising the two local $d_{zx}$ orbitals in the Ir-${\mathrm{O}}_2$-Ir bond plane, which conflicts with the equal superposition of $d_{xy}, d_{yz}$, and $d_{zx}$ orbitals in the $J_{\mathrm{eff}}=1/2$ wave function produced by strong spin-orbit coupling. The results of resonant inelastic x-ray scattering measurements and the electronic structure calculations are fully consistent with the collapse of the $J_{\mathrm{eff}}=1/2$ state. The competition between the spin-orbital-entangled $J_{\mathrm{eff}}=1/2$ state and molecular-orbital formation is most likely universal in honeycomb-based Kitaev materials.

Figure 1

Crystal structure of $\beta -{\mathrm{Li}}_2{\mathrm{IrO}}_3$. (a) and (c) Local structure around an ${\mathrm{IrO}}_6$ octahedron at ambient pressure and 2.6(1) GPa, respectively. (b) and (d) Hyperhoneycomb network of Ir atoms. X, Y, and Z denote the three types of Ir-Ir bonds. (e) Local structure around an ${\mathrm{IrO}}_6$ octahedron in the high-pressure phase at 4.4(1) GPa. (f) Ir sublattice in the high-pressure phase. The dimerized bond is shown in red. The crystal structures are illustrated using vesta software [47].

Figure 2

RIXS spectra of $\beta -{\mathrm{Li}}_2{\mathrm{IrO}}_3$ under pressure recorded at room temperature. The data from the polycrystalline sample (bottom) were collected at ambient pressure, and the data at 2.6(1) GPa (top) were collected after the sample was depressurized from 7.4(1) GPa. The spectra are normalized by the high-energy tail above 5 eV and shown with arbitrary offsets. The horizontal dashed lines represent the guide baselines, obtained by subtracting a constant background from each spectrum. (b) The comparison of RIXS spectra between the ambient and high-pressure phases above $P_{\mathrm{S}}$. The spectra are normalized by the high-energy tails above 5 eV to highlight the change by pressure. The low-energy shoulder of the elastic line in the 6.0-GPa spectrum is likely attributed to the scattering from the Be gasket or pressure medium.

Figure 3

Calculated density of states (DOS) for Ir $5d$ states. (a) DOS for the ambient pressure phase ($Fddd$). The Ir $t_{2g}$ orbitals are resolved into $J_{\mathrm{eff}}=1/2$ and 3/2 states. The two $J_{\mathrm{eff}}$ = 3/2 states, (1) and (2), are primarily composed of $J_{\mathrm{eff}}^z=1/2$ and $J_{\mathrm{eff}}^z$ = 3/2 characters, respectively. (b) DOS for the high-pressure phase ($C2/c$). The $d_{zx}$ orbital is directed along the ${\mathrm{Ir}}_2$ dimer bond. The other $t_{2g}$ orbitals, $d_{xy}$ and $d_{yz}$, are entangled by spin-orbit coupling and denoted as “entangled $xy-yz$.” The total DOS includes the contributions from oxygen $2p$ states.